Hard squares with negative activity
نویسندگان
چکیده
We show that the hard-square lattice gas with activity z = −1 has a number of remarkable properties. We conjecture that all the eigenvalues of the transfer matrix are roots of unity. They fall into groups (“strings”) evenly spaced around the unit circle, which have interesting number-theoretic properties. For example, the partition function on an M × N lattice with periodic boundary condition is identically 1 when M and N are coprime. We provide evidence for these conjectures from analytical and numerical arguments.
منابع مشابه
Application of Non-Linear Functions at Distribution of Output SINR Gaussian Interference Channels
We have examined the convergence behavior of the LSCMA in some simple environments. Algorithms such as Multi¬ Target CMA, Multistage CMA, and Iterative Least Squares with Projection can be used for this purpose. The results presented here can form a basis for analysis of these multi-signal extraction techniques. Clearly, the variance and distribution of output SINR obtained with the LSCMA is al...
متن کاملExperimental and Theoretical Study of Electroconvection in Homeotropic Nematic Liquid Crystal
Electroconvection patterns have been studied in a homeotropic nematic liquid crystal, experimental and theoretical, with unusual combination of material parameters, negative conductivity and positive dielectric permittivity anisotropies. Exploring the complete phase diagram in the (U, q) space three distinct morphologies, rolls and squares, soft squares and hard squares have been identified. We...
متن کاملSimulated Annealing with Levy Distribution for Fast Matrix Factorization-Based Collaborative Filtering
Matrix factorization is one of the best approaches for collaborative filtering, because of its high accuracy in presenting users and items latent factors. The main disadvantages of matrix factorization are its complexity, and being very hard to be parallelized, specially with very large matrices. In this paper, we introduce a new method for collaborative filtering based on Matrix Factorization ...
متن کاملApproximate L0 constrained non-negative matrix and tensor factorization
Non-negative matrix factorization (NMF), i.e. V ≈ WH where both V, W and H are non-negative has become a widely used blind source separation technique due to its part based representation. The NMF decomposition is not in general unique and a part based representation not guaranteed. However, imposing sparseness both improves the uniqueness of the decomposition and favors part based representati...
متن کاملHard Squares with Negative Activity on Cylinders with Odd Circumference
Let Cm,n be the graph on the vertex set {1, . . . ,m} × {0, . . . , n − 1} in which there is an edge between (a, b) and (c, d) if and only if either (a, b) = (c, d ± 1) or (a, b) = (c ± 1, d), where the second index is computed modulo n. One may view Cm,n as a unit square grid on a cylinder with circumference n units. For odd n, we prove that the Euler characteristic of the simplicial complex Σ...
متن کامل